Can I make edits made in edit mode appear in animations?
Yes, there is a way, called shape keys.

Other question, where shape keys are explained: How to animate a mesh that changes through editing?

Select an original pose and do the first shpe key, then do your facial expression, or whatever, in editmode and add another shape key. One Shape key by, eg facial expression. By changing an expressions value, the expression whichs vallue you make the highest dominates. Shape keys can be animated by holding the mouse over the value and pressing "i", setting a keyframe.